 
Summary: MEASURES OF PSEUDORANDOMNESS FOR FINITE
SEQUENCES: TYPICAL VALUES
N. ALON, Y. KOHAYAKAWA, C. MAUDUIT, C. G. MOREIRA, AND V. R¨ODL
Abstract. Mauduit and S´ark¨ozy introduced and studied certain nu
merical parameters associated to finite binary sequences EN {1, 1}N
in order to measure their `level of randomness'. Those parameters, the
normality measure N(EN ), the welldistribution measure W(EN ), and
the correlation measure Ck(EN ) of order k, focus on different combinato
rial aspects of EN . In their work, amongst others, Mauduit and S´ark¨ozy
(i) investigated the relationship among those parameters and their min
imal possible value, (ii) estimated N(EN ), W(EN ), and Ck(EN ) for
certain explicitly constructed sequences EN suggested to have a `pseu
dorandom nature', and (iii) investigated the value of those parameters
for genuinely random sequences EN .
In this paper, we continue the work in the direction of (iii) above
and determine the order of magnitude of N(EN ), W(EN ), and Ck(EN )
for typical EN . We prove that, for most EN {1, 1}N
, both W(EN )
and N(EN ) are of order
